At a school fundraiser for every 9 boxes of chocolate sold, you earn 6 points. If you were to sell 18 boxes, how many points would you have earned.

Question

Can u show me how do it step by step.

Answer 1

Zoey, since I don't know how old you are, I am going to show you the beginner way and the more advanced way to do this.

 

First, the beginner.  For every 9 boxes, you earn 6 points. This means that:

 

b b b b b b b b b = p p p p p p

 

If you sold 18 boxes, then you sold b b b b b b b b b b b b b b b b b b.  How many times does the original 9 boxes appear?

 

(b b b b b b b b b) (b b b b b b b b b). There are two sets of 9 boxes. Since we said that b b b b b b b b b = p p p p p p, then (b b b b b b b b b) (b b b b b b b b b) = (p p p p p p) (p p p p p p), so 18 boxes earns us 12 points!

 

The more advanced way to do it is by setting up a proportion, or two equal ratios.

 

First 9 boxes gets us 6 points. As a proportion, that is 9 to 6 or 9/6.

 

Since we are doing boxes to points, if we let p = the number of points we earn, then our second ratio is 18 to p, or 18/p.

 

Setting up the proportion, we have 9/6 = 18/p.  

 

Cross multiplying, we get 9p = 6(18), or 9p = 108.  Dividing both sides by 9, we get p = 12, so we earn 12 points for selling 18 boxes.

 

Hope this helps!